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Enzo and Zahra are playing a game. Their scores for five games are shown in the table below.

\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{6}{|c|}{Enzo's and Zahra's Scores} \\
\hline Enzo's Scores & 39 & 47 & 46 & 50 & 38 \\
\hline Zahra's Scores & 37 & 33 & 45 & 30 & 45 \\
\hline
\end{tabular}

Enzo's mean score is 44. Zahra's mean score is 38. How much greater is the mean absolute deviation for Zahra's scores than for Enzo's scores?

A. 1.2
B. 4.4
C. 5.6
D. 6.0

Sagot :

GinnyAnswer
To determine how much greater the mean absolute deviation (MAD) is for Zahra's scores compared to Enzo's scores, let's follow these steps:

1. Understand Mean Absolute Deviation (MAD):
The mean absolute deviation is calculated by taking the average of the absolute differences between each score and the mean score of the data set.

2. Calculate the Mean Absolute Deviation for Enzo:
Enzo's scores are 39, 47, 46, 50, and 38. His mean score is provided as 44.
- First, find the absolute deviations from the mean for each score:
[tex]\( |39 - 44|, |47 - 44|, |46 - 44|, |50 - 44|, |38 - 44| \)[/tex].
- This gives us: [tex]\( |39 - 44| = 5, |47 - 44| = 3, |46 - 44| = 2, |50 - 44| = 6, |38 - 44| = 6 \)[/tex].
- Now, calculate the average (mean) of these absolute deviations:
[tex]\[ \frac{5 + 3 + 2 + 6 + 6}{5} = \frac{22}{5} = 4.4 \][/tex]
- So, the MAD for Enzo's scores is 4.4.

3. Calculate the Mean Absolute Deviation for Zahra:
Zahra's scores are 37, 33, 45, 30, and 45. Her mean score is provided as 38.
- First, find the absolute deviations from the mean for each score:
[tex]\( |37 - 38|, |33 - 38|, |45 - 38|, |30 - 38|, |45 - 38| \)[/tex].
- This gives us: [tex]\( |37 - 38| = 1, |33 - 38| = 5, |45 - 38| = 7, |30 - 38| = 8, |45 - 38| = 7 \)[/tex].
- Now, calculate the average (mean) of these absolute deviations:
[tex]\[ \frac{1 + 5 + 7 + 8 + 7}{5} = \frac{28}{5} = 5.6 \][/tex]
- So, the MAD for Zahra's scores is 5.6.

4. Determine the difference in MAD:
- The difference between Zahra's MAD and Enzo's MAD is:
[tex]\[ 5.6 - 4.4 = 1.2 \][/tex]

Therefore, the mean absolute deviation for Zahra's scores is 1.2 units greater than for Enzo's scores. The correct answer is:

1.2
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